1. Field of the Invention
The present invention relates to a decision method for deciding a mask pattern and exposure conditions used in an exposure apparatus, a storage medium, and an information processing apparatus.
2. Description of the Related Art
In recent years, miniaturization of semiconductor devices has progressed, and it is difficult to transfer (resolve) a pattern by an exposure apparatus. Hence, in order to cope with miniaturization of semiconductor devices, an exposure apparatus adopts a super-resolution technique such as off-axis illumination or OPC (Optical Proximity Correction) so as to optimize an illumination shape (effective light source distribution) upon illuminating a mask pattern and mask. The illumination shape is a light intensity distribution formed on a pupil plane of an illumination optical system, and is also an angle distribution of light which illuminates a mask.
To optimize the illumination shape, a layout pattern (target pattern) of a device, evaluation positions of a transfer pattern (optical image), and evaluation items (size, DOF, exposure margin, and the like) at the evaluation positions are set. Next, a transfer pattern is calculated while changing the illumination shape, and values of evaluation items (evaluation values) at the evaluation positions of the transfer pattern are calculated. Then, calculations of the transfer pattern and evaluation values are repeated until the evaluation values satisfy an allowable range or the number of times of change of the illumination shape reaches a predetermined count. The illumination shape is numerically expressed. For example, in case of annular illumination having a given intensity, the illumination shape is expressed by a function having inner σ and outer σ as parameters (variables), and these parameters are optimized using a Monte Carlo method or the like. Even when a mask pattern remains the same, if a different illumination shape is used, a different transfer pattern is formed. For this reason, by changing the illumination pattern, a transfer pattern deviates from a target pattern. Hence, the OPC is required to match the transfer pattern with the target pattern. The OPC is executed every time the illumination shape is changed or when the illumination shape is changed by a given amount. However, the OPC is limited to correction of a shape of a transfer pattern such as a line width, edge shift, and image shift, and cannot apply correction of an image contrast, depth of focus, and the like, which are decided by the illumination shape and are associated with resolving performance.
U.S. Pat. No. 6,563,566 has proposed a technique for setting a pattern to be formed on a substrate (wafer), and calculating an optimized mask pattern and illumination shape by a mathematical approach. The technique of U.S. Pat. No. 6,563,566 analytically calculates solutions (mask pattern and illumination shape) in place of iterative calculations. In the technique of U.S. Pat. No. 6,563,566, the OPC is not applied, but a pattern to be formed on a substrate and an optimized mask pattern are different, and this technique is an optimization technique of the illumination pattern including correction of the mask pattern in the broad sense.
Also, Japanese Patent Laid-Open Nos. 2009-93138 and 2009-94109 have proposed a technique for inserting an auxiliary pattern (a self non-resolving pattern) into a main pattern (a self resolving pattern) so as to relax resolving performance differences between miniaturized density patterns and isolated patterns. In Japanese Patent Laid-Open Nos. 2009-93138 and 2009-94109, the auxiliary pattern is inserted at a peak (Laplacian peak) position of a two-dimensional TCC approximate aerial image.
However, the technique of U.S. Pat. No. 6,563,566 has the advantage that solutions can be analytically calculated, but it has to limit an evaluation item to a tilt of an optical image, and also has to limit a type of pattern to be formed on a substrate to one. In this manner, the technique of U.S. Pat. No. 6,563,566 is not practical since it has the disadvantage of low degrees of freedom.
In the technique of Japanese Patent Laid-Open Nos. 2009-93138 and 2009-94109, generation conditions required to generate an auxiliary pattern, that is, how to insert an auxiliary pattern with respect to a given illumination shape are fixed in advance. Therefore, the technique of Japanese Patent Laid-Open Nos. 2009-93138 and 2009-94109 does not always decide optimal illumination conditions and mask pattern.